Self-consistent inhomogeneous steady states in Hamiltonian mean-field dynamics
Bibliographic record
Abstract
Long-lived quasistationary states, associated with stationary stable solutions of the Vlasov equation, are found in systems with long-range interactions. Studies of the relaxation time in a model of N globally coupled particles moving on a ring, the Hamiltonian mean-field model (HMF), have shown that it diverges as N(γ) for large N, with γ1.7 for some initial conditions with homogeneously distributed particles. We propose a method for identifying exact inhomogeneous steady states in the thermodynamic limit, based on analyzing models of uncoupled particles moving in an external field. For the HMF model, we show numerically that the relaxation time of these states diverges with N with the exponent γ ~/= 1. The method, applicable to other models with globally coupled particles, also allows an exact evaluation of the stability limit of homogeneous steady states. In some cases, it provides a good approximation for the correspondence between the initial condition and the final steady state.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.001 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".